A mathematical model for fibro-proliferative wound healing disorders

Abstract

The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor mediators. Biologically, these conditions are poorly understood and current medical treatments are thus unreliable.In this paper, the authors apply an existing deterministic mathematical model for fibroplasia and wound contraction in adult mammalian dermis (Olsen et al., J. theor. Biol. 177, 113-128, 1995) to investigate key clinical problems concerning these healing disorders. A caricature model is proposed which retains the fundamental cellular and chemical components of the full model, in order to analyse the spatiotemporal dynamics of the initiation, progression, cessation and regression of fibro-contractive diseases in relation to normal healing. This model accounts for fibroblastic cell migration, proliferation and death and growth-factor diffusion, production by cells and tissue removal/decay.Explicit results are obtained in terms of the model processes and parameters. The rate of cellular production of the chemical is shown to be critical to the development of a stable pathological state. Further, cessation and/or regression of the disease depend on appropriate spatiotemporally varying forms for this production rate, which can be understood in terms of the bistability of the normal dermal and pathological steady states-a central property of the model, which is evident from stability and bifurcation analyses.The work predicts novel, biologically realistic and testable pathogenic and control mechanisms, the understanding of which will lead toward more effective strategies for clinical therapy of fibro-proliferative disorders.

Bone ingrowth on the surface of endosseous implants. Part 2: Theoretical and numerical analysis

“…Note that this simplified model is similar to the one proposed in Dale et al (1995) and Olsen et al (1996) for the study of wound healing disorders and presents equivalent mathematical properties. Here, however, we have performed a systematic study of all the possible travelling wave solutions that can appear depending on the parameter values and initial conditions.…”

A mechanochemical model for normal and abnormal dermal wound repair

“…In this case, our analysis shows that reducing K~, the linear rate at which cells secrete growth factor, can cause the disease to regress back to the normal dermal state. More detailed analysis of this model ( [4]) d e t ermines analytically how the bifurcation values of q depend on the other parameters in the model. This provides a clinically-testable method to help reduce this type of fibroproliferative disorder.…”

“…showing progression to pathological steady state (a), and cessation and regression for the case where IE, in reduced to zero after a certain time (b). See [4] for parameter values.…”

“…where x(c, n) = a/(/3 + c)~, and cr,p, I', &, IE, and y are positive constants (see [4] for full details). This caricature model has two uniform steady states, (n, c) = (0, 0), (K, 0) corresponding, respectively, to the trivial, or non-healing, state, and the normal dermal state.…”

Pattern Formation And Wound Healing

“…We have considered a mechanochemical model for dermal wound contraction with the aim of understanding how fibroproliferative and fibrocontractive abnormal healing occurs. The model has been used to make predictions on how keliod scarring may be reduced (Olsen et al, 1996).…”